Two-photon dilepton production in proton-proton collisions: two alternative approaches

We investigate different methods to incorporate the effect of photons in hard processes. We compare two different approaches used for calculating cross sections for two-photon $p p \to l^+ l^- X$ process. In one of the approaches photon is treated as a collinear parton in the proton. In the second approach recently proposed a $k_T$-factorization method is used. We discuss how results of the collinear parton model depend on the initial condition for the QCD evolution and discuss an approximate treatment where photon is excluded from the combined QCD-QED evolution. We demonstrate that it is not necessary to put photon into the evolution equation as often done recently but it is sufficient to use a simplified approach in which photon couples to quarks and antiquarks which by themselves undergo DGLAP evolution equations. We discuss sensitivity of the results to the choice of structure function parametrization and experimental cuts in the $k_T$-factorization approach. A new optimal structure function parametrization is proposed. We compare results of our calculations with recent experimental data for dilepton production and find that in most cases the contribution of the photon-photon mechanism is rather small. We discuss how to enhance the photon-photon contribution. We also compare our results to those of recent measurements of exclusive and semi-exclusive $e^+ e^-$ pair production with certain experimental data by the CMS collaboration.